Gen 1 Blizzard being 90% accurate and initially having a 30% chance to freeze (lowered to 10% internationally and in Stadium), was a symptom of how the game was conceived as a single player campaign. Link battles were something that were introduced into Red and Green very late into development.
It was intended to be a late-game powerful move that was either a great asset to the player if they used the TM, or a major threat when Lorelei's Lapras used it in the Elite Four challenge.

From Gen 2 onwards, there was a bigger focus on battles against trainers or in controlled rule sets like Battle Tower, where you can't just spam items to compensate for bad strategy or disadvantageous situations.
Naturally, moves and their effects and probabilities all got re-thought here. Aside from Blizzard itself being nerfed, the Freeze status was also nerfed so that a Pokémon had a 10% chance to thaw out (20% in Gen 3 onwards).
Many other things were retooled too, like your speed stat affecting the critical hit ratio, the "special" stat being split into separate special attack and special defense stats, the introduction of dark and steel types, the changing of type effectiveness particularly for psychic and ghost types, and how OHKO moves function.
They also started considering special cases like Earthquake hitting a Pokémon that's used Dig, or Thunder hitting a target that's used Fly.